The Supreme Court justices seemed ready Monday to limit the ability of U.S. courts to hear civil lawsuits alleging corporate complicity in human rights abuses overseas, but there was uncertainty about how tightly to shut the door.

Lawyer Paul L. Hoffman faced an uphill task in trying to persuade the justices to allow such suits. The United States has been a leader in a worldwide trend toward “universal justice” for people and corporations that engage in human rights atrocities, he said.

Allowing U.S. courts to consider such suits “should be given the chance to work,” Hoffman said.

The human rights case was the first of the Supreme Court’s new term. But it was the continuation of months of debate about whether a founding-era law, the Alien Tort Statute, can be used as a vehicle for pressing human rights lawsuits.

The law allows federal courts to hear “any civil action by an alien for a tort only, committed in violation of the law of nations or a treaty of the United States.” But it was rarely invoked until the 1970s.

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The court first accepted the case last year to decide whether the law applies to corporations or only individuals. But at oral arguments in February, it became clear that some conservative justices wondered whether it should apply to any acts committed overseas, and the court ordered new arguments.

It was clear Monday that those concerns remained. The case at hand involves about a dozen Nigerians now living in the United States who allege that Royal Dutch Petroleum, the parent company of Shell Oil, aided and abetted the Ni­ger­ian government in torturing and killing people protesting the company’s operations in the Ogoni region during the 1990s.

“Why does this case belong in the courts of the United States when it has nothing to do with the United States, other than the fact that a subsidiary of the defendant has a big operation here?” he asked.

Other justices had similar questions, and Hoffman acknowledged that the best link was that the Nigerians had fled here.

“The plaintiffs in this case received asylum in the United States because of the human rights violations alleged in the complaint,” Hoffman said. “They sued the defendants for their role in these human rights violations in U.S. courts because the defendants are here and subject to the general personal jurisdiction of our courts.”

Justice Anthony M. Kennedy worried that allowing such a suit would mean that “if a U.S. corporation commits an international law violation in the United States, that U.S. corporation can be sued in any court in the world.”

Shell’s lawyer, Kathleen Sullivan, said that is why the court should rule broadly that actions overseas should not be judged in American courts.

“This case has nothing to do with the United States,” Sullivan said. “It’s Nigerian plaintiffs suing an English and Dutch company for activity alleged to have aided and abetted the Nigerian government for conduct taking place entirely within Nigeria.”

But some justices were reluctant to accept Shell’s sweeping interpretation. The law was prompted by an attack on a French diplomat in Philadelphia, and a 1795 opinion by Attorney General William Bradford said it covered conduct on the high seas.

“If, when the statute was passed, it applied to pirates, the question to me is, who are today’s pirates?” Justice Stephen G. Breyer said. “And if Hitler isn’t a pirate, who is? And if, in fact, an equivalent torturer or dictator who wants to destroy an entire race in his own country is not the equivalent of today’s pirate, who is?”

But finding a proper limit was difficult. Kagan wondered if the plaintiffs should first have tried to pursue their claims in the U.K. and the Netherlands, the homes of two divisions of the company.

The Obama administration’s proposed solution did not draw much support. Solicitor General Donald B. Verrilli Jr. said that Shell should win the case because “there just isn’t any meaningful connection to the United States.”

The government’s position has infuriated human rights groups. Verrilli has tried to straddle the issue, saying there could be some states where U.S. courts should entertain such suits, without being very specific.

The stance raised an obvious question: What if the corporation involved was an American one, rather than a foreign one?

“We haven’t taken a position on that question in this case because we think that the court ought to proceed incrementally here,” Verrilli replied.